Finite Impulse Response ( FIR ) Filters
Maurice Bellanger · Digital Signal Processing · 2024
Digital finite impulse response (FIR) filters are discrete linear time-invariant systems in which an output number, representing a sample of the filtered signal, is obtained by weighted summation of a finite set of input numbers, representing samples of the signal to be filtered. The coefficients of the weighted summation constitute the filter's impulse response and only a finite number of them take nonzero values. The fact that transfer functions with linear phase can be realized is an important property which is exploited in spectral analysis or in data-transmission applications. A first iterative approach consists of using the discrete Fourier transform, which is calculated efficiently by a fast algorithm. Limitation of the number of bits in the coefficients of a filter produces a change in the frequency response, which appears as the superposition of an error function.